599 research outputs found
Right and Left Modules over the Frobenius Skew Polynomial Ring in the F-Finite Case
The main purposes of this paper are to establish and exploit the result that,
over a complete (Noetherian) local ring of prime characteristic for which
the Frobenius homomorphism is finite, the appropriate restrictions of the
Matlis-duality functor provide an equivalence between the category of left
modules over the Frobenius skew polynomial ring that are Artinian as
-modules and the category of right -modules that are Noetherian as
-modules.Comment: 16 pages, to appear in the Mathematical Proceedings of the Cambridge
Philosophical Society. This revised version includes two additionl references
and points out that some of the results have been obtained independently by
M. Blickle and G. Boeckl
Large Abdominal Wall Endometrioma Following Laparoscopic Hysterectomy
Although extrapelvic endometriosis is rare, it should be considered in the diagnosis of the female patient with an abdominal mass and pain who has had a previous surgical procedure
Constructing Fluorogenic Bacillus Spores (F-Spores) via Hydrophobic Decoration of Coat Proteins
Background: Bacterial spores are protected by a coat consisting of about 60 different proteins assembled as a biochemically complex structure with intriguing morphological and mechanical properties. Historically, the coat has been considered a static structure providing rigidity and mainly acting as a sieve to exclude exogenous large toxic molecules, such as lytic enzymes. Over recent years, however, new information about the coat’s architecture and function have emerged from experiments using innovative tools such as automated scanning microscopy, and high resolution atomic force microscopy. Principal Findings: Using thin-section electron microscopy, we found that the coat of Bacillus spores has topologically specific proteins forming a layer that is identifiable because it spontaneously becomes decorated with hydrophobic fluorogenic probes from the milieu. Moreover, spores with decorated coat proteins (termed F-spores) have the unexpected attribute of responding to external germination signals by generating intense fluorescence. Fluorescence data from diverse experimental designs, including F-spores constructed from five different Bacilli species, indicated that the fluorogenic ability of F-spores is under control of a putative germination-dependent mechanism. Conclusions: This work uncovers a novel attribute of spore-coat proteins that we exploited to decorate a specific layer imparting germination-dependent fluorogenicity to F-spores. We expect that F-spores will provide a model system to gai
Asymptotic Behavior of Ext functors for modules of finite complete intersection dimension
Let be a local ring, and let and be finitely generated
-modules such that has finite complete intersection dimension. In this
paper we define and study, under certain conditions, a pairing using the
modules \Ext_R^i(M,N) which generalizes Buchweitz's notion of the Herbrand
diference. We exploit this pairing to examine the number of consecutive
vanishing of \Ext_R^i(M,N) needed to ensure that \Ext_R^i(M,N)=0 for all
. Our results recover and improve on most of the known bounds in the
literature, especially when has dimension at most two
Surface code quantum computing by lattice surgery
In recent years, surface codes have become a leading method for quantum error
correction in theoretical large scale computational and communications
architecture designs. Their comparatively high fault-tolerant thresholds and
their natural 2-dimensional nearest neighbour (2DNN) structure make them an
obvious choice for large scale designs in experimentally realistic systems.
While fundamentally based on the toric code of Kitaev, there are many variants,
two of which are the planar- and defect- based codes. Planar codes require
fewer qubits to implement (for the same strength of error correction), but are
restricted to encoding a single qubit of information. Interactions between
encoded qubits are achieved via transversal operations, thus destroying the
inherent 2DNN nature of the code. In this paper we introduce a new technique
enabling the coupling of two planar codes without transversal operations,
maintaining the 2DNN of the encoded computer. Our lattice surgery technique
comprises splitting and merging planar code surfaces, and enables us to perform
universal quantum computation (including magic state injection) while removing
the need for braided logic in a strictly 2DNN design, and hence reduces the
overall qubit resources for logic operations. Those resources are further
reduced by the use of a rotated lattice for the planar encoding. We show how
lattice surgery allows us to distribute encoded GHZ states in a more direct
(and overhead friendly) manner, and how a demonstration of an encoded CNOT
between two distance 3 logical states is possible with 53 physical qubits, half
of that required in any other known construction in 2D.Comment: Published version. 29 pages, 18 figure
A statistical downscaling framework for environmental mapping
In recent years, knowledge extraction from data has become increasingly popular, with many numerical forecasting models, mainly falling into two major categories—chemical transport models (CTMs) and conventional statistical methods. However, due to data and model variability, data-driven knowledge extraction from high-dimensional, multifaceted data in such applications require generalisations of global to regional or local conditions. Typically, generalisation is achieved via mapping global conditions to local ecosystems and human habitats which amounts to tracking and monitoring environmental dynamics in various geographical areas and their regional and global implications on human livelihood. Statistical downscaling techniques have been widely used to extract high-resolution information from regional-scale variables produced by CTMs in climate model. Conventional applications of these methods are predominantly dimensional reduction in nature, designed to reduce spatial dimension of gridded model outputs without loss of essential spatial information. Their downside is twofold—complete dependence on unlabelled design matrix and reliance on underlying distributional assumptions. We propose a novel statistical downscaling framework for dealing with data and model variability. Its power derives from training and testing multiple models on multiple samples, narrowing down global environmental phenomena to regional discordance through dimensional reduction and visualisation. Hourly ground-level ozone observations were obtained from various environmental stations maintained by the US Environmental Protection Agency, covering the summer period (June–August 2005). Regional patterns of ozone are related to local observations via repeated runs and performance assessment of multiple versions of empirical orthogonal functions or principal components and principal fitted components via an algorithm with fully adaptable parameters. We demonstrate how the algorithm can be extended to weather-dependent and other applications with inherent data randomness and model variability via its built-in interdisciplinary computational power that connects data sources with end-users
The Bond-Algebraic Approach to Dualities
An algebraic theory of dualities is developed based on the notion of bond
algebras. It deals with classical and quantum dualities in a unified fashion
explaining the precise connection between quantum dualities and the low
temperature (strong-coupling)/high temperature (weak-coupling) dualities of
classical statistical mechanics (or (Euclidean) path integrals). Its range of
applications includes discrete lattice, continuum field, and gauge theories.
Dualities are revealed to be local, structure-preserving mappings between
model-specific bond algebras that can be implemented as unitary
transformations, or partial isometries if gauge symmetries are involved. This
characterization permits to search systematically for dualities and
self-dualities in quantum models of arbitrary system size, dimensionality and
complexity, and any classical model admitting a transfer matrix representation.
Dualities like exact dimensional reduction, emergent, and gauge-reducing
dualities that solve gauge constraints can be easily understood in terms of
mappings of bond algebras. As a new example, we show that the (\mathbb{Z}_2)
Higgs model is dual to the extended toric code model {\it in any number of
dimensions}. Non-local dual variables and Jordan-Wigner dictionaries are
derived from the local mappings of bond algebras. Our bond-algebraic approach
goes beyond the standard approach to classical dualities, and could help
resolve the long standing problem of obtaining duality transformations for
lattice non-Abelian models. As an illustration, we present new dualities in any
spatial dimension for the quantum Heisenberg model. Finally, we discuss various
applications including location of phase boundaries, spectral behavior and,
notably, we show how bond-algebraic dualities help constrain and realize
fermionization in an arbitrary number of spatial dimensions.Comment: 131 pages, 22 figures. Submitted to Advances in Physics. Second
version including a new section on the eight-vertex model and the correction
of several typo
Compactification, topology change and surgery theory
We study the process of compactification as a topology change. It is shown
how the mediating spacetime topology, or cobordism, may be simplified through
surgery. Within the causal Lorentzian approach to quantum gravity, it is shown
that any topology change in dimensions may be achieved via a causally
continuous cobordism. This extends the known result for 4 dimensions.
Therefore, there is no selection rule for compactification at the level of
causal continuity. Theorems from surgery theory and handle theory are seen to
be very relevant for understanding topology change in higher dimensions.
Compactification via parallelisable cobordisms is particularly amenable to
study with these tools.Comment: 1+19 pages. LaTeX. 9 associated eps files. Discussion of disconnected
case adde
- …